“Coherence–incoherence” transition in ensembles of nonlocally coupled chaotic oscillators with nonhyperbolic and hyperbolic attractors

Abstract

We consider in detail similarities and differences of the “coherence–incoherence” transition in ensembles of nonlocally coupled chaotic discrete-time systems with nonhyperbolic and hyperbolic attractors. As basic models we employ the Henon map and the Lozi map. We show that phase and amplitude chimera states appear in a ring of coupled Henon maps, while no chimeras are observed in an ensemble of coupled Lozi maps. In the latter, the transition to spatio-temporal chaos occurs via solitary states. We present numerical results for the coupling function which describes the impact of neighboring oscillators on each partial element of an ensemble with nonlocal coupling. Varying the coupling strength we analyze the evolution of the coupling function and discuss in detail its role in the “coherence–incoherence” transition in the ensembles of Henon and Lozi maps.